Philippe L. Toint

Formulation and solution strategies for nonparametric nonlinear stochastic programs, with an application in finance

  • Fabian Bastin
  • Philippe L. Toint
  • Cinzia Cirillo
    • Categories Finance and Economics, Nonlinear Optimization, Stochastic Programming Tags , , ,

    We consider a class of stochastic programming models where the uncertainty is classically represented using parametric distributions families. The parameters are then usually estimated together with the optimal value of the problem. However, misspecification of the underlying random variables often leads to irrealistic results when little is known about their true distributions. We propose to … Read more

    LANCELOt_simple, a simple interface to LANCELOT B

  • Nicholas I. M. Gould
  • Dominique Orban
  • Philippe L. Toint
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Optimization Software and Modeling Systems Tags , ,

    We describe LANCELOT_simple, an interface to the LANCELOT B nonlinear optimization package within the GALAHAD} library (Gould, Orban, Toint, 2003) which ignores problem structure. The result is an easy-to-use Fortran 90 subroutine, with a small number of intuitively interpretable arguments. However, since structure is ignored, the means of presenting problems to the solver limited and … Read more

    Multi-Secant Equations, Approximate Invariant Subspaces and Multigrid Optimization

  • Serge Gratton
  • Philippe L. Toint
    • Categories Optimization of Systems modeled by PDEs, Unconstrained Optimization Tags , , ,

    New approximate secant equations are shown to result from the knowledge of (problem dependent) invariant subspace information, which in turn suggests improvements in quasi-Newton methods for unconstrained minimization. It is also shown that this type of information may often be extracted from the multigrid structure of discretized infinite dimensional problems. A new limited-memory BFGS using … Read more

    A Retrospective Trust-Region Method for Unconstrained Optimization

  • Fabian Bastin
  • Vincent Malmedy
  • Philippe L. Toint
  • Mélodie Mouffe
  • Dimitri Tomanos
    • Categories Unconstrained Optimization Tags , , ,

    We introduce a new trust-region method for unconstrained optimization where the radius update is computed using the model information at the current iterate rather than at the preceding one. The update is then performed according to how well the current model retrospectively predicts the value of the objective function at last iterate. Global convergence to … Read more

    A multilevel algorithm for solving the trust-region subproblem

  • Philippe L. Toint
  • Melissa Weber-Mendonca
  • Dimitri Tomanos
    • Categories Infinite Dimensional Optimization, Optimization of Systems modeled by PDEs, Unconstrained Optimization Tags , , ,

    We present a multilevel numerical algorithm for the exact solution of the Euclidean trust-region subproblem. This particular subproblem typically arises when optimizing a nonlinear (possibly non-convex) objective function whose variables are discretized continuous functions, in which case the different levels of discretization provide a natural multilevel context. The trust-region problem is considered at the highest … Read more

    Adaptive cubic overestimation methods for unconstrained optimization

  • Coralia Cartis
  • Nicholas I. M. Gould
  • Philippe L. Toint
    • Categories Unconstrained Optimization Tags , , ,

    An Adaptive Cubic Overestimation (ACO) algorithm for unconstrained optimization is proposed, generalizing at the same time an unpublished method due to Griewank (Technical Report NA/12, 1981, DAMTP, Univ. of Cambridge), an algorithm by Nesterov & Polyak (Math. Programming 108(1), 2006, pp 177-205) and a proposal by Weiser, Deuflhard & Erdmann (Optim. Methods Softw. 22(3), 2007, … Read more

    A recursive trust-region method in infinity norm for bound-constrained nonlinear optimization

  • Serge Gratton
  • Philippe L. Toint
  • Melissa Weber-Mendonca
  • Mélodie Mouffe
    • Categories Bound-constrained Optimization, Nonlinear Optimization, Unconstrained Optimization Tags , , ,

    A recursive trust-region method is introduced for the solution of bound-constrained nonlinear nonconvex optimization problems for which a hierarchy of descriptions exists. Typical cases are infinite-dimensional problems for which the levels of the hierarchy correspond to discretization levels, from coarse to fine. The new method uses the infinity norm to define the shape of the … Read more

    Nonlinear programming without a penalty function or a filter

  • Nicholas I. M. Gould
  • Philippe L. Toint
    • Categories Constrained Nonlinear Optimization, Nonlinear Systems and Least-Squares, Systems governed by Differential Equations Optimization Tags , , ,

    A new method is introduced for solving equality constrained nonlinear optimization problems. This method does not use a penalty function, nor a barrier or a filter, and yet can be proved to be globally convergent to first-order stationary points. It uses different trust-regions to cope with the nonlinearities of the objective function and the constraints, … Read more

    A Brief History of Filter Methods

  • Roger Fletcher
  • Sven Leyffer
  • Philippe L. Toint
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    We consider the question of global convergence of iterative methods for nonlinear programming problems. Traditionally, penalty functions have been used to enforce global convergence. In this paper we review a recent alternative, so-called filter methods. Instead of combing the objective and constraint violation into a single function, filter methods view nonlinear optimization as a biobjective … Read more

    Numerical Experience with a Recursive Trust-Region Method for Multilevel Nonlinear Optimization

  • Serge Gratton
  • Annick Sartenaer
  • Philippe L. Toint
    • Categories Nonlinear Optimization, Systems governed by Differential Equations Optimization, Unconstrained Optimization Tags , , , ,

    We consider an implementation of the recursive multilevel trust-region algorithm proposed by Gratton, Sartenaer, Toint (2004), and provide significant numerical experience on multilevel test problems. A suitable choice of the algorithm’s parameters is identified on these problems, yielding a very satisfactory compromise between reliability and efficiency. The resulting default algorithm is then compared to alternative … Read more